Problem: Rewrite as a simplified fraction. ${0.4\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 48.8888...\\ 10x &= 4.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 44}$ ${x = \dfrac{44}{90}} $ ${x = \dfrac{22}{45}} $